Teacher Tune-ups are concise explanations prepared for teachers by math experts.
Teachers raise GREAT questions about mathematics! Select from those listed below to read a response from a math educator or mathematician. To recommend an additional Teacher Tune-up, complete the form at the bottom of this page.
Ratio and Proportional Relationships
What's the difference between a ratio and a fraction, and why should I care?
What are the shortcomings of cross-multiplication?
What is unit rate as opposed to rate?
Why is "per" so important?
How is "scaling" related to proportional relationships?
Why is –1 x –1 = 1?
Number Line Models for Sums and Differences with Integers
Difference, Distance, and the Truth about Absolute Value
What are the three basic ways we think of division?
Making Sense of Division of Fractions
Delaying "Invert and Multiply"
Multiplication makes things bigger and division makes things smaller, right? Well, not so fast...
Expressions and Equations
The Algebraic Alphabet: Unknowns, Variables, and Parameters
How do you generate equations from patterns?
Algebraic Terms Sixth and Seventh Graders Encounter
What are ways to represent different start points and different speeds?
How can focusing on expressions prevent students from rushing to answer-getting?
Getting Insight from Graphs
What is a net? What can you learn from a net?
Triangles and Constraints
Drawing Triangles: Conventions and Mechanics
Statistics and Probability
How should students describe the center and spread of a data set?
We use dot plots, histograms, and box plots...which one to use?
Probability Basics for Middle-School Teachers
Variability and Randomness within Classroom Activities
Recording Data: Setting Up the System
Using T-Tables to Study Patterns